The field of the invention is nuclear magnetic resonance imaging methods and systems. More particularly, the invention relates to a method for correcting for gradient non-linearities in k-space. It will be appreciated, however, that the invention is also amenable to other like applications.
Magnetic resonance imaging (MRI) is a diagnostic imaging modality that does not rely on ionizing radiation. Instead, it uses strong uniform static magnetic fields, radio-frequency (RF) pulses of energy and magnetic field gradient waveforms. More specifically, MRI is a non-invasive procedure that uses nuclear magnetization and radio waves for producing internal pictures of a subject. Data concerning an area of interest on the subject under investigation is acquired during repetitive excitations of the magnetic resonance (MR) device.
When utilizing MRI to produce images, a technique is employed to obtain MRI signals from specific locations in the subject. Typically, the region that is to be imaged (region of interest) is scanned by a sequence of MRI measurement cycles, which vary according to the particular localization method being used. The resulting set of received nuclear magnetic resonance (NMR) signals are digitized and processed to reconstruct the image using one of many well-known reconstruction techniques. To perform such a scan it is necessary to discriminate NMR signals from specific locations in the subject. This is accomplished by employing gradient magnetic fields denoted Gx, Gy, and Gz. A magnetic field gradient is a variation in the magnetic field with respect to position along the x, y and z axes. By controlling the strength of these gradients during each NMR cycle, the spatial distribution of spin excitation can be altered and the location is encoded in the resulting NMR signals.
MRI uses time-varying gradient magnetic fields to encode spatial position in the received NMR signal. If the gradient fields are linear, it can be shown that the received NMR signal is equal to the value of the Fourier transform of the imaged object at some spatial frequency, and the received signal over time maps to a trajectory through spatial-frequency space, or k-space. The trajectory path is determined by the time integral of the applied gradient waveforms. Each data point of the NMR signal indicates the phase and amplitude of a spatial frequency and a full experiment yields a set of observed data points that specify the NMR image as the sum of these weighted spatial frequencies. More succinctly, a complete set of MRI data samples k-space sufficiently to allow reconstruction of the imaged object via the inverse Fourier transform. This relation between received NMR signal and spatial-frequency space has led to the development of the theory of Fourier imaging which has been applied to and forms the basis of much of NMR imaging.
Fourier imaging relies on linear gradients. Truly linear gradient magnetic fields are infeasible due to constraints on physical space within the main magnet, gradient heating limits, and other practical considerations. In practice, gradients are not spatially linear. Using Fourier reconstruction on data acquired with non-linear gradients can result in image artifacts. Non-linear gradients can cause a spatially variant image distortion and a low-frequency amplitude modulation. If the perturbation from a linear field is known, then the distortion and the modulation can be corrected. The modulation can be corrected by multiplying the resulting images by the inverse of the modulation function. The distortions can be corrected by generating a new image based on values interpolated from the original image. This image-based correction of gradient non-linearity is known as gradwarp and is described in Glover et al. in U.S. Pat. No. 4,591,789. It requires not only that the gradient non-linearity be known, but that it be temporally constant over the course of an experiment. One situation where this approach does not work is the reconstruction of NMR data from a sample that is moving through the MRI system. In this case, although the non-linearity is constant relative to the magnet coordinates, the non-linearity varies relative to the sample coordinates (and thus the image coordinates) as the sample moves through regions of varying gradient linearity.
Stepped or continuous table motion can be used to image a field of view (FOV) larger than the region of instrument sensitivity. Data acquired at different table positions, can be combined to form a single image. Any variations in gradient linearity in the direction of table motion will result in image artifacts. Typically, these artifacts are avoided by limiting data acquisition to the most linear region of the gradient fields. This restriction limits the maximum table velocity. If the limits on data acquisition could be relaxed, scan times could be reduced significantly. Traditional image domain methods to correct for gradient non-linearities are incompatible with the moving table methods since data is acquired at a range of table positions.